Thank you for that thorough response, Andy. My main issue is noise at those levels and I am shooting .jpg. I know, I know, RAW is better, but, as I mentioned, I'm not a pro and I don't have a lot of time to process the photos from the games.
If you want to use the "out of camera" photos you could shoot RAW, pull the RAW images into DxO PhotoLab, and "edit" the first image - simply by turning on DeepPrime 3 or the DeepPrime XD (depends on how bad the noise is), then right click - Copy "Copy Correction Settings", highlight the rest of your shots (whether it be 10 or 500), right click "Paste Correction Settings", and it will apply whatever you have done to the first one to the rest. This process shouldn't take more than 5 minutes maximum, probably less (assuming no viewing or culling of other shots.
Then select all images and "Export to Disc" as JPEG, and walk away for a coffee. When you return you will have every shot in JPEG (with all noise removed) with lens corrections, a degree of camera+lens specific sharpening applied, and whatever else you wanted. You could then review the photos, cull them out, and if you wanted to display or print some, then do selective further processing on those only.
DxO PhotoLab (if you don't have it) is IMO excellent, especially for noise reduction and raw conversion (including excellent camera and lens corrections) and is available as a full functioning trial for 30 days (at least it was 9 months ago) to test it out before committing. May be cheaper than buying new gear and I think you might find the process to be surprisingly quick and easy.